\( \lim _ { x \rightarrow 0 ^ { + } } ( x ^ { 2 } \sin ( x ) ) ^ { \frac { 1 } { x } } \)

a. \( \lim _{x \rightarrow 1} \frac{3-\sqrt{10-x}}{x-1} \)

\( \int _ { - 2 } ^ { 2 } \int _ { - 2 } ^ { 2 } \cos ( x y ) d x d y \)

\( \int \frac { x ^ { 2 } - 2 x - 1 } { ( x - 1 ) ^ { 2 } ( x ^ { 2 } + 1 ) } d x \)

10. (3 points) Find the derivative of \( y=x^{2 x} \) \( \begin{array}{ll}\text { (A) } y^{\prime}=(2 \ln (x)+2) & \text { (B) } y^{\prime}=x^{2 x} \cdot(2 \ln (x)+1) \\ \text { C } y^{\prime}=2 x \cdot x^{2 x-1} & \text { (D) } y^{\prime}=x^{2 x} \cdot(2 \ln (x)+2)\end{array} \)

\( \int \frac { u ^ { 2 } } { 1 + u ^ { 4 } } d u \)